Trustless groups of unknown order

Abstract: Groups of unknown order have cryptographic applications including time-lock puzzles, verifiable delay functions, and accumulators. While a trusted authority might simply choose an RSA group and be done with it, in the trustless setting the problem of generating cryptographically secure unknown-order groups is much more subtle. We will explore this problem, comparing two concrete constructions - class groups of quadratic imaginary fields, and Jacobians of hyperelliptic curves - with a special focus on the surprisingly complicated issues of security levels and appropriate key sizes.

cryptography and security

Audience: researchers in the discipline

( video )

Comments: Benjamin Smith is a research scientist with INRIA, the French national computer science research institute, and an adjunct professor at École Polytechnique. His research is focused on number-theoretic cryptographic algorithms, especially in (hyper)elliptic curve cryptography and isogeny based cryptography.

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Selected Areas in Cryptography 2020

Series comments: See the conference web page for more information about the program, registration, etc.

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